A111041 Numbers m such that 2*m^2 + 25 is prime.

3, 6, 12, 18, 21, 27, 33, 36, 39, 51, 54, 63, 66, 69, 81, 96, 114, 138, 159, 168, 177, 183, 204, 216, 219, 228, 231, 234, 237, 252, 258, 276, 279, 282, 312, 324, 369, 381, 393, 402, 411, 423, 426, 429, 432, 447, 462, 483, 492, 507, 516, 531, 546, 561, 564, 573

Offset

1,1

Comments

Necessarily m = 0 (mod 3) because: (a) if m = 3k+1 then 2*m^2 + 25 = 2*(3k+1)^2 + 25 = 2*(9*k^2 + 6*k + 1) + 25 = 18*k^2 + 12*k + 27 = 0 mod 3; (b) if m = 3k-1 then 2*m^2 + 25 = 2*(3k-1)^2 + 25 = 2*(9*k^2 - 6*k + 1) + 25 = 18*k^2 - 12*k + 27 = 0 mod 3; (c) while m = 3k then 2*m^2 + 25 = 2*(3k)^2 + 25 = 18*k^2 + 25 = 1 mod 3, which can be prime. - Jonathan Vos Post, Oct 06 2005

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

If m=96 then (2*m^2) + 25 = 18457 (prime).

Mathematica

Select[Range[600], PrimeQ[2 #^2+25]&] (* Harvey P. Dale, Jul 29 2025 *)

Prog

(Magma) [n: n in [0..600] | IsPrime(2*n^2+25)]; // Vincenzo Librandi, Nov 13 2010
(PARI) is(n)=isprime(2*n^2+25) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

Sequence in context: A162845 A239708 A038588 * A079830 A160744 A160738

Adjacent sequences: A111038 A111039 A111040 * A111042 A111043 A111044

Keyword

nonn,easy

Author

Parthasarathy Nambi, Oct 05 2005

Extensions

More terms from Jonathan Vos Post, Oct 06 2005

Status

approved